bettyboop8904
Can someone please help me with some integral homework before I shoot the crap out of my calculus book pretty please?! Equation in the forum
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bettyboop8904
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\[\int\limits_{}^{}\ln (\sqrt[3]{x})\]
That is x to the 3 root
mathsmind
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hi there
bettyboop8904
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hello = )
jim_thompson5910
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it might help to think of the cube root of x as x^(1/3)
jim_thompson5910
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then use the power rule
mathsmind
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ok do u want me to solve it or should i tell u how to do it
bettyboop8904
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ok I got as far to as thinking of x^(1/3) lol
jim_thompson5910
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now use the rule that
integral of x^n = (1/(n+1))*x^(n+1)
mathsmind
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if u solve it i give u medal and if i do so you give me one
bettyboop8904
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so do u mean put 1/3 in front of the ln of stuff and then put it in front of the entire integral? bc that's what I did and it said it was wrong = (
jim_thompson5910
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there's no ln involved here
mathsmind
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u=x^1/3
bettyboop8904
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ok maybe you should write the whole thing out cuz now you're just confusing me, please, thank you
jim_thompson5910
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does this rule look familiar
|dw:1360297226043:dw|
jim_thompson5910
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sry the +C is nearly cut off
bettyboop8904
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no yeah i already know that lol we're in the chapter of integration by parts and there is a ln involved it's in the front of the x^(1/3)
anonymous
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not to interrupt, but i think the starting point here is
\[\frac{1}{3}\int \ln(x)dx\] which you do either by parts or by memory
jim_thompson5910
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oh my bad, i didn't see the ln at the very beginning
just thought it was cube root of x
mathsmind
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its ok
anonymous
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since \(\ln(x)\) is a very common function, it might be benificial just to memorize
\[\int \ln(x)dx=x\ln(x)-x\] you can check by differentiation
bettyboop8904
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yes that's what i did. oh damn nvm hahaha i think i get it I keep getting it confused that the derivative of ln is 1/x and we don't know the integral of ln yet so we have to do integration by parts lol
anonymous
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your answer is therefore
\[\frac{1}{3}\left(x\ln(x)-x \right)\]
mathsmind
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you can use taylor series to integrate this easily
mathsmind
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but with z=x+1
bettyboop8904
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you guys were a great help! ty! = )
anonymous
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i would memorize it
just like remembering that
\[\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}\]so while your fellow classmates are integrating by parts, you just write down the answer
mathsmind
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i won't recommend that method
mathsmind
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what about\[\int\limits \ln e^{^{x ^{2}}}dx\]
mathsmind
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or
mathsmind
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\[\int\limits \ln(x^x)dx\]
mathsmind
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or
mathsmind
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\[\int\limits \ln(x^2+2x+1)dx\]
mathsmind
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so these are 3 examples that can't be used by just memorizing the specific case
mathsmind
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so basically use integration by parts like ur class mates